solve the quadratic equation
xsquared - 2x - 3 = 0
What is
(x-3)(x+1) ?
To solve the quadratic equation x^2 - 2x - 3 = 0, we can use the quadratic formula which is given by:
x = (-b±√(b^2-4ac))/2a
In this equation, a, b, and c represent the coefficients of the quadratic equation.
Comparing the equation x^2 - 2x - 3 = 0 with the quadratic formula, we have:
a = 1
b = -2
c = -3
Now, we can substitute these values into the quadratic formula and solve for x.
x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / (2(1))
Simplifying further:
x = (2 ± √(4 + 12)) / 2
x = (2 ± √(16)) / 2
x = (2 ± 4) / 2
This gives us two solutions for x:
x1 = (2 + 4) / 2 = 6 / 2 = 3
x2 = (2 - 4) / 2 = -2 / 2 = -1
Therefore, the solutions to the quadratic equation x^2 - 2x - 3 = 0 are x = 3 and x = -1.
To solve the quadratic equation x^2 - 2x - 3 = 0, we can use the quadratic formula. The quadratic formula states that for a quadratic equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing this with our given equation x^2 - 2x - 3 = 0, we have a = 1, b = -2, and c = -3. Now, let's substitute these values into the quadratic formula and solve for x:
x = (-(-2) ± √((-2)^2 - 4*1*(-3))) / (2*1)
x = (2 ± √(4 + 12)) / 2
x = (2 ± √16) / 2
x = (2 ± 4) / 2
Now, we have two possible solutions:
1. x = (2 + 4) / 2 = 6 / 2 = 3
2. x = (2 - 4) / 2 = -2 / 2 = -1
Therefore, the solutions to the quadratic equation x^2 - 2x - 3 = 0 are x = 3 and x = -1.